Question: ${\sqrt[3]{2916} = \text{?}}$
Solution: $\sqrt[3]{2916}$ is the number that, when multiplied by itself three times, equals $2916$ First break down $2916$ into its prime factorization and look for factors that appear three times. So the prime factorization of $2916$ is $2\times 2\times 3\times 3\times 3\times 3\times 3\times 3$ Notice that we can rearrange the factors like so: $2916 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = (3\times 3\times 3) \times (3\times 3\times 3) \times 2\times 2$ So $\sqrt[3]{2916} = \sqrt[3]{3\times 3\times 3} \times \sqrt[3]{3\times 3\times 3} \times \sqrt[3]{2\times 2}$ $\sqrt[3]{2916} = 3\times 3 \times \sqrt[3]{2\times 2}$ $\sqrt[3]{2916} = 9 \sqrt[3]{4}$